Imaging through a light scattering medium or imaging an object within a scattering medium is one of the most challenging problems in optical signal processing, and has significant importance in tomography and image processing, and has significant importance in tomography and image formation in biological tissues. One popular "first light" approach to solving this problem is based on the principle of the first arriving light, wherein a time gate is used to separate the information carrying light, or the first light, from the noisy light, namely the subsequent scattered light. In a specific implementation by Mantic and Duguay, a hologram was used as a time gating processor. See "Ultrahigh-speed photography of picosecond light pulses and echoes", Applied Optics, 10, pp. 2162-2170, (1971). Since then, different time gating techniques have been used for performing the time gating, involving electronic and real time holograms, Kerr and Raman cells, and spatial filtering techniques yielding improved signal-to-noise ratios. Unfortunately, these first light techniques require ultrafast pulses and sophisticated instrumentation for ultrafast imaging, thus making them expensive to implement.
An alternative to the first light approach is to use the photon density approach. In this case, the pulsed light is replaced by ultrafast modulated light. When such light propagates within a scattering medium, the intensity of the light, as well as its phase, is determined by the properties of the media. The photon density waves in different scattering media have an analogy to light propagation in materials with different indices of refraction. It has been proven that the photon density waves obey Snell's law of refraction. See M. A. O'Leary et al., "Refraction of Diffuse Density Waves", Physical Review Letters, Vol. 69, No. 18. Therefore, when the photon density waves pass through two different scattering media, one embedded inside the other, the waves refract as if they were passing through materials with different indices of refraction. The result is that by monitoring the output wave, in terms of amplitude and phase, much can be determined about the nature of the object inside the scattering media. In essence, the method of detecting variations in the phases due to different indices of refraction using interferometric techniques, can also be applied to photon density waves passing through scattering media. The difference is that in the interferometric approach, the variation is between the phase of the reference and the signal beams, while in the photon density approach, the variation is between the phase of the modulation of the reference and signal beams.